1. Field of the Invention
The present invention relates generally to medical, industrial, scientific, and multi-media imaging and related arts, and more particularly, to a method and system for processing, reconstructing, or deconstructing acquired N-dimensional frequency-space data or image/audio/video-space data (inverse frequency-space data, in general), by the application of an arbitrary-resolution and parallelizable processing, reconstruction, and deconstruction method.
2. Description of Related Art
In many areas of science and technology, the processing and analysis of data depend on time-frequency and spatial-frequency analyses. This is true in everything from molecular analysis to image, audio, and video processing and compression. The primary techniques for such tasks are the Fast Fourier Transform (FFT) and wavelet transforms. For example, the FFT is the process of choice for many image/audio/video compression techniques (JPEG images, MP3 audio, MPEG video, etc.), and wavelets are the basis for JPEG2000 image compression. The FFT is the most popular technique for time-frequency or spatial-frequency analysis, but it is known for certain limitations—in particular, the FFT permits only specific sets of frequencies, which are all integer multiples of a single fundamental frequency, 1/Ns, where Ns is typically the number of sample points in the time or space domain. To get high resolution in FFT frequency analysis, the number of samples Ns must be correspondingly large. Wavelets offer better resolution, but are typically limited to logarithmically-spaced frequencies.
Since the FFT is limited to specific sets of frequencies, any non-uniform frequency-space data must be aligned with such frequencies. (Non-uniform data is, for example, associated with spiral and radial MM scans (magnetic resonance imaging), and CT scans (computed tomography) in general. In the field of MRI/fMRI, spiral and radial scanning patterns are typically faster than other types of patterns, and the images produced are less susceptible to errors caused by motion during the scanning process.) The most common technique for this alignment of non-uniform data is known as gridding. Although gridding is fast computationally, it is known in the art for generating image artifacts (image errors) that corrupt the reconstructed images. Newer techniques, such as the Non-Uniform FFT (NUFFT) or conjugate gradient, or traditional techniques such as back-projection approaches, attempt to eliminate the need for gridding, but these techniques are generally approximation techniques, using approaches such as least squares, interpolation, or iteration. In complex cases, iterative techniques such as conjugate gradient will converge to an answer slowly, or not at all—so, although the reconstructed images are more accurate, they might require minutes or hours of computation. The goal, then, is to find a way to transform data, such that the results exhibit no gridding artifacts, or negligible gridding artifacts, and such that the results can be computed quickly.
An additional problem in the field is that current reconstruction techniques typically generate images that are small by today's standards. For example, whereas a typical consumer camera can output raw images of sizes such as 4,600-by-3,500 pixels or larger, fMRI machines typically output raw images of size 64-by-64 pixels, and MM machines typically reconstruct raw images of size 256-by-256 pixels or 512-by-512 pixels. Such low-resolution images are associated with frequency-space based medical imaging technologies in particular, including MRI/fMRI, CT, ultrasound, PET (positron emission tomography), and SPECT (single-photon emission computed tomography). These raw images are typically scaled to larger sizes by interpolation techniques, so that radiologists can better see the results of the scans, but interpolation is an approximation technique that increases the image size on the display by essentially stretching the low-resolution image, not by generating a large raw image. The goal, then, is to find a way to process frequency-space data, so that the raw reconstructed images can be arbitrarily large. In the case of medical imaging, this can allow radiologists to get a better look at areas of interest, and would also allow them to “zoom in” to enlarge a particular sub-region.
An additional problem in the field is that the FFT requires input dimensions that are powers of 2. When this condition is not met, the size of the input data must be increased to a power of 2. Since powers of 2 grow exponentially large, the input data similarly grows exponentially, which then results in lengthier computations and slower computation times. The goal, then, is to find a way to process data, so that the reconstructions and deconstructions do not require input sizes that are exponential powers, thus resulting in efficient computations, particularly for large data sets.
An additional problem in the field is that true 3-dimensional (“true 3D”, also known as “full 3D”) or true N-dimensional (multi-dimensional) frequency-space data is associated with slow computations in industrial, medical, and scientific applications. For example, for MM, true 3D scans offer higher resolution than the more common technique of multiple and adjacent 2D scans, but it is less popular in practice largely due to the slower scans and reconstructions associated with this imaging technique. 3D and multi-dimensional scans and frequency-space data are also associated with scientific applications, such as protein analysis, and with industrial applications, such as ground penetrating radar, seismic analysis, cartography, and oil, gas, and water exploration. (It is noted here that such applications also frequently process data in fewer than 3 dimensions, but the 3D and multi-dimensional cases are the most challenging in terms of computation speed.) The goal, then, is to find a way to process 3D or multi-dimensional frequency-space data, so that the reconstructed images, or data, can be computed quickly.